Extensions of labeling algorithms for multi‐objective uncertain shortest path problems

Abstract

We consider multi‐objective shortest path problems in which the edge lengths are uncertain. Different concepts for finding so‐called robust efficient solutions for multi‐objective robust optimization exist. In this article, we consider multi‐scenario efficiency, flimsily and highly robust efficiency, and point‐based and set‐based minmax robust efficiency. Labeling algorithms are an important class of algorithms for multi‐objective (deterministic) shortest path problems. We analyze why it is, for most of the considered concepts, not straightforward to use labeling algorithms to find robust efficient solutions. We then show two approaches to extend a generic multi‐objective label correcting algorithm for these cases. We finally present extensive numerical results on the performance of the proposed algorithms.

An Efficient Label-setting Algorithm for the Bi-objective Shortest Path Problem

“…In order to compare our results with benchmarks algorithms solving the BSP -the bounded Label Setting algorithm (blSET) (Raith, 2010) and the pulse algorithm (Duque et al, 2015) -computational experiments have been performed on instances from the 9 th DIMACS challenge. Three graphs have been used.…”

“…(Raith and Ehrgott, 2009) has shown that this approach is efficient and proposed a comparison of the solution strategies for finding all efficient paths. (Raith, 2010) focuses on label-correcting and labelsetting algorithm (bLSET) and propose an acceleration technique, improving the efficiency of these algorithms. He showed that it is not always necessary to continue the search to the target node to confirm that it is dominated.…”

“…Some numerical results are given in section 3 in order to test the different exploration strategies and a parameter of the algorithm. Then computational experiments compare our proposed method to the bLSET algorithm developed by (Raith, 2010) and the Pulse algorithm developed by (Duque et al, 2015). Finally section 4 concludes the paper and gives some future work directions.…”

New advances and applications in deterministic and stochastic network optimization

“…Silva et al develop and evaluate an alternative routing scheme for the Robust Network Loading problem with demand uncertainty. The scheme, denoted by named k ‐adaptive, is based on the fact that the decision‐maker chooses k second‐stage solutions and then commits to one of them only after realization of the uncertainty.…”

“…Raith et al [5] consider multi-objective shortest path problems in which the edge lengths are uncertain. Different concepts for finding so-called robust efficient solutions for multi-objective robust optimization exist.…”